One obvious attempt to solve this equation is . The solution set to this equation is . One of these is maximum and the other is minimum. Note that there are infinitely many maximums and minimums, as the function has a period of .

One obvious attempt to solve this equation is . The solution set to this equation is . One of these is maximum and the other is minimum. Note that there are infinitely many maximums and minimums, as the function has a period of .

Yup, these are solutions to f'(x)=0, but how can we know they're the only solutions, and maximum or minimum of the function ?